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let u(x)=(u_1(x), u_2(x)) be a solution of the differential system u_1' = g_1(u_1,u_2), u_2' =g_2 (u_1,u_2)....

let u(x)=(u_1(x), u_2(x)) be a solution of the differential system u_1' = g_1(u_1,u_2), u_2' =g_2 (u_1,u_2). Show that if u(x_0 +w)=u(x_0) for some w>0, then u(x+w) =u(x) for all x>=x_0, i.e., u(x) is periodic of period w   

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